LOGISTIC曲线模型在颈椎病物理治疗过程中的特征表达及与疗效的关系★

背景：在先导研究中验证了LOGISTIC模型能够充分地解释颈椎病物理治疗中疼痛症状缓解过程的变化信息，是理想的数学表达模型。 目的：分析颈椎病物理治理过程LOGISTIC曲线模型中各数学特征与治疗效果之间的关系，进一步探讨LOGISTIC模型对颈椎病物理治疗过程的表达能力。 方法：对一组连续接受10次物理治疗的90例颈椎病根性疼痛患者在治疗过程中连续进行目测类比法疼痛评定，采用前期建立的LOGISTIC曲线模型，分别求得各病例回归曲线的数学特征值，包括拐点和曲率极值点。探讨各数学特征值与治疗有效性和缓解幅度之间的关联。 结果与结论：治疗过程中疼痛的缓解程度与拐点位置和第二曲率极值点位置呈负相关(r=-0.460，P < 0.001；r=-0.598，P < 0.001)；与第一曲率极值点位置相关性无统计学意义(r=0.075， P=0.481)。说明拐点、第二曲率极值点出现的越早，治疗全过程所能达到的缓解幅度越大；第一曲率极值点出现的位置与治疗中的疼痛缓解幅度无明显关联性。有效病例与无效病例组间拐点与第二曲率极值点位置不同，差异有显著性意义，第一曲率极值点两组间差异无显著性意义。ROC分析可见以第二曲率极值点和拐点作为有效与否的判断指标都能获得较高的曲线下面积，约登指数可以达到0.54~0.64，具备一定的判断能力。说明LOGISTIC曲线模型的数学特征值与物理治疗效果存在明显的关联，LOGISTIC曲线模型对颈椎病物理治疗的过程特征表达充分。 关键词：颈椎病；物理治疗；疼痛评定；LOGISTIC模型；治疗效果；数字化骨科技术

Relationship between therapeutic effect of physical therapy on cervical rediculopathy patients and characteristics described by the LOGISTIC regression model

BACKGROUND: In previous study, the LOGISTIC model has been established and showed its superiority in describing the physical therapy processes on cervical radiculopathy. OBJECTIVE: To analysis relation between the therapeutic effects and the math characters given by the LOGISTIC model, and to demonstrate the effectiveness of LOGISTIC model in describing the physical therapy processes on cervical radiculopathy. METHODS: Multiple physical therapies were administered to 90 cervical radiculopathy patients with pain for 10 sessions. A visual analogue scale was used to measure the pain intensity before each time. Calculate the inflexion and the curvature extremum point of each patient from the LOGISTIC model. Statistical analysis was performed for demonstrating the relation between the therapeutic effects and the math characters. RESULTS AND CONCLUSION: The pain relief and location of inflection point was negatively correlated with the second extreme point of curvature (r=-0.460, P < 0.001; r=-0.598, P < 0.001); which had no significance with the first extreme point of curvature (r=0.075, P=0.481). It reveled that the earlier appearance of inflection point and the second extreme point of curvature, the most pain relief. There was no obvious correlation between the first extreme point of curvature location and the pain relief. The location of inflexion point and the curvature extremum point were different between the effective cases and the ineffective case, but the differences of the first extreme point of curvature had no significance between two groups. ROC analysis showed that using inflection point and the second extreme point of curvature as judgment indexes, greater area under curve could be obtained, and the Youden index was 0.54-0.64, which exhibited judgment capacity. The LOGISTIC model can describe the characters of physical therapy processes on cervical radiculopathy sufficiently.